Difference between revisions of "6"
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! Property or family !! Parameter values !! First few members of the family !! Proof of satisfaction/membership/containment | ! Property or family !! Parameter values !! First few members of the family !! Proof of satisfaction/membership/containment | ||
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− | | [[perfect number]]: number <math>n</math> such that the divisor sum function of <math>n</math> is <math>2n</math> || first perfect number || {{#lst:perfect number|list}} || divisor sum is <math>1 + 2 + 3 + 6 = 12 = 2(6)</math> | + | | [[satisfies property::perfect number]]: number <math>n</math> such that the divisor sum function of <math>n</math> is <math>2n</math> || first perfect number || {{#lst:perfect number|list}} || divisor sum is <math>1 + 2 + 3 + 6 = 12 = 2(6)</math> |
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− | | [[primorial]]: product of the first few prime numbers || product of the first two prime numbers (if we start the indexing from the zeroth primorial, which is an empty product and evaluates to 1, it is the ''third'' in the list) || {{#lst:primorial|list}} || The first two primes are 2 and 3, and their product is 6. | + | | [[satisfies property::primorial]]: product of the first few prime numbers || product of the first two prime numbers (if we start the indexing from the zeroth primorial, which is an empty product and evaluates to 1, it is the ''third'' in the list) || {{#lst:primorial|list}} || The first two primes are 2 and 3, and their product is 6. |
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− | | [[factorial]]: product of the first few natural numbers || product of the first three natural numbers (if we start the indexing from the zeroth factorial, which is an empty product and evaluates to 1, it is the ''fourth'' in the list) || {{#lst:factorial|list}} || <math>1 \cdot 2 \cdot 3 = 6</math> | + | | [[satisfies property::factorial]]: product of the first few natural numbers || product of the first three natural numbers (if we start the indexing from the zeroth factorial, which is an empty product and evaluates to 1, it is the ''fourth'' in the list) || {{#lst:factorial|list}} || <math>1 \cdot 2 \cdot 3 = 6</math> |
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− | | [[lcm of all numbers so far]]: lcm of the first few natural numbers || lcm of the first three natural numbers || {{#lst:lcm of all numbers so far|list}} || <math>\operatorname{lcm} \{ 1,2,3 \} = 6</math>. | + | | [[satisfies property::lcm of all numbers so far]]: lcm of the first few natural numbers || lcm of the first three natural numbers || {{#lst:lcm of all numbers so far|list}} || <math>\operatorname{lcm} \{ 1,2,3 \} = 6</math>. |
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Latest revision as of 18:00, 3 July 2012
This article is about a particular natural number.|View all articles on particular natural numbers
Summary
Factorization
The number 6 has the following factorization, with prime factors 2 and 3:
Properties and families
Property or family | Parameter values | First few members of the family | Proof of satisfaction/membership/containment |
---|---|---|---|
perfect number: number such that the divisor sum function of is | first perfect number | divisor sum is | |
primorial: product of the first few prime numbers | product of the first two prime numbers (if we start the indexing from the zeroth primorial, which is an empty product and evaluates to 1, it is the third in the list) | 1, 2, 6, 30, 210, 2310 View list on OEIS | The first two primes are 2 and 3, and their product is 6. |
factorial: product of the first few natural numbers | product of the first three natural numbers (if we start the indexing from the zeroth factorial, which is an empty product and evaluates to 1, it is the fourth in the list) | 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, [SHOW MORE] View list on OEIS | |
lcm of all numbers so far: lcm of the first few natural numbers | lcm of the first three natural numbers | 1, 1, 2, 6, 12, 60, 60, 420, [SHOW MORE] View list on OEIS | . |
Arithmetic functions
Function | Value | Explanation |
---|---|---|
Euler totient function | 2 | The Euler totient function is . |
universal exponent | 2 | The universal exponent is . |
divisor count function | 4 | where the first 1s in both factors are the multiplicities of the prime divisors. |
divisor sum function | 12 | times equals . |
Mobius function | 1 | The number is square-free and has an even number of prime divisors (2 prime divisors). |